A patch antenna is often utilized as a low-profile and low-cost multi-constellation global navigation satellite system (GNSS) antenna due to its planar configuration and ease of integration with circuit boards. To shrink the size of the antenna, it is well known in the art to use ceramic material as the substrate. Typical considerations of using ceramics are its high DK (ε′, dielectric constant) and low dielectric loss. Depending on the compounds and composites, the DK of the ceramics can vary from the range of approximately 4 to several hundred. To cover the dual-band requirements of a typical GNSS system, two or more stacked patches are required to resonate at each frequency. For circular patches, the fundamental mode of operation is TM11 mode, which has an upper-hemisphere radiation pattern that works well for GNSS applications. Using the well known cavity model, the fundamental mode's resonance frequency is given by
                    (                  f          r                )            11        =                            χ          11                ⁢        c                    2        ⁢        π        ⁢                                  ⁢                  a          eff                ⁢                              ɛ            eq                                ,where χ11 represents the first zero of the derivative of the Bessel function, J1′(χ)=0, aeff is the effective radius of the circular patch disk, εeq is the equivalent dielectric constant and c is the speed of light. Using the same material as substrate, the sizes of the two patches are significantly different: the top one resonating at the L1 band is roughly about 77% of the L2 patch at the bottom layer. Therefore, the overall lateral size of the antenna is determined by the bottom radiator. Using ceramic as substrate reduces the size of the antenna, but as a noted disadvantage, it also narrows the bandwidth since the quality factor Q of the resonant antenna is inversely proportional to the volume it physically occupy according to Chu-Harrington limit for electrically small antennas.